2009/09/29 by Stéphane Gaïffas, Gaïffas, Stéphane, Agathe Guilloux +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.0909.5342
arxiv created 2009/09/29 · openalex publication_date 2009/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We consider the problem of statistical learning for the intensity of a counting process with covariates. In this context, we introduce an empirical risk, and prove risk bounds for the corresponding empirical risk minimizers. Then, we give an oracle inequality for the popular algorithm of aggregation with exponential weights. This provides a way of constructing estimators that are adaptive to the smoothness and to the structure of the intensity. We prove that these estimators are adaptive over anisotropic Besov balls. The probabilistic tools are maximal inequalities using the generic chaining mechanism, which was introduced by Talagrand (2006), together with Bernstein's inequality for the underlying martingales.